Keep tax returns, as well as supporting documents like W-2 forms, receipts, and real estate closing statements for seven years. The IRS may audit you within three years if it suspects good-faith errors; six years if it believes you underreported your income by at least 25%; and unlimited time if you did not file a return or filed a fraudulent one.

Investment records

Keep as long as you own the securities, plus another seven years [Rich]. You'll need them to prove capital gains and losses.

Bank statements

One month. You just need these long enough to check the accuracy of the transactions [Williams]. Unless the statement is your only record for a tax-related transaction, there's no need to keep them longer. Plus, your bank will have them available online.